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<p>Initial conditions can drive coexisting multistable patterns of a single neuron and the collective behaviors of the coupled neural network. In order to explore their roles in a class of memristive ReLU-type Hopfield neural network (mRHNN), this paper presents the memristor synapse-coupled model consisting of two identical memristive mRHNNs. The bi-mRHNN model with no equilibrium point is confirmed, and complete synchronization is proved using the Lyapunov method. To quantify synchronization transitions, peak differences, phase portraits, and normalized mean synchronization errors are analyzed numerically. Simulations reveal that coupling strength and, notably, the initial conditions of the memristor significantly influence the emergence of various synchronous behaviors. Furthermore, a digital hardware circuit is developed to implement these meaningful phenomena experimentally. Finally, a ring-structured network of 100 mRHNNs is constructed, where initial condition-induced coherent, incoherent, and chimera states are observed. These findings will offer new insights into the information processing mechanisms of complex neural networks.</p>

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Initial condition-induced synchronization and chimera state in memristor synapse-coupled memristive Hopfield neural networks

  • 期刊论文

  • 发表日期：

    2025年5月22日

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  • Chengjie Chen,
  • Fuhong Min,
  • Yunzhen Zhang,
  • Han Bao

摘要

Initial conditions can drive coexisting multistable patterns of a single neuron and the collective behaviors of the coupled neural network. In order to explore their roles in a class of memristive ReLU-type Hopfield neural network (mRHNN), this paper presents the memristor synapse-coupled model consisting of two identical memristive mRHNNs. The bi-mRHNN model with no equilibrium point is confirmed, and complete synchronization is proved using the Lyapunov method. To quantify synchronization transitions, peak differences, phase portraits, and normalized mean synchronization errors are analyzed numerically. Simulations reveal that coupling strength and, notably, the initial conditions of the memristor significantly influence the emergence of various synchronous behaviors. Furthermore, a digital hardware circuit is developed to implement these meaningful phenomena experimentally. Finally, a ring-structured network of 100 mRHNNs is constructed, where initial condition-induced coherent, incoherent, and chimera states are observed. These findings will offer new insights into the information processing mechanisms of complex neural networks.